Tesi etd-06212016-153250 |
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Tipo di tesi
Tesi di laurea magistrale
Autore
ANDOLINA, GIAN MARCELLO
URN
etd-06212016-153250
Titolo
Topological properties of Shiba Chain with orbital degree of freedom
Dipartimento
FISICA
Corso di studi
FISICA
Relatori
relatore Prof. Vicari, Ettore
relatore Prof. Simon, Pascal
relatore Prof. Simon, Pascal
Parole chiave
- Majorana fermions
- Shiba chain
- topological phases
- topological superconductivity
Data inizio appello
21/07/2016
Consultabilità
Completa
Riassunto
Topological superconductors are new materials that can host exotic quasiparticles at their edges called Majorana fermions (MFs) . MFs are particles which are their own anti-particles. They may be useful for quantum computation since they obey non-abelian statistics.
In order to achieve experimentally topological superconductivity a convenient direction is to combine well established materials to engineer this exotic superconductivity. One promising approach is to utilise magnetic impurities on top of a superconductor that can host MFs. This system can be theoretically described using the Shiba chain Hamiltonian in the dilute limit, or using the quantum wire Hamiltonian in the dense limit. In the literature, the intermediate regime has not been studied. In this work we aim to filling this gap.
In this thesis, we study more complex and realistic models to describe a chain of magnetic atoms on top of a superconductor by taking into account the different impurity orbital degrees of freedom. Therefore, due to the impurity orbital overlap one has a 1D conduction band on top of the superconductor coexisting with the magnetic moments that can create a 1D Shiba band into the superconductor. The main original result of this thesis is the derivation of an effective low-energy Kitaev-like Hamiltonian that describes the system as two 1D coupled channels.
Thanks to this model we achieved the main goal of this thesis: we are able to derive the phase diagram of the system by computing numerically the winding number w that shows that the system has different topological phases characterized by the presence (or absence) of multiple MFs. We discuss the role of disorder showing that the existence of multiple MF is related with the presence of the effective time-reversal symmetry. Finally, we study how the phase diagram changes in the small magnetization limit.
Our final statement is that the system can be topological and can host multiple MFs for certain conditions.
In order to achieve experimentally topological superconductivity a convenient direction is to combine well established materials to engineer this exotic superconductivity. One promising approach is to utilise magnetic impurities on top of a superconductor that can host MFs. This system can be theoretically described using the Shiba chain Hamiltonian in the dilute limit, or using the quantum wire Hamiltonian in the dense limit. In the literature, the intermediate regime has not been studied. In this work we aim to filling this gap.
In this thesis, we study more complex and realistic models to describe a chain of magnetic atoms on top of a superconductor by taking into account the different impurity orbital degrees of freedom. Therefore, due to the impurity orbital overlap one has a 1D conduction band on top of the superconductor coexisting with the magnetic moments that can create a 1D Shiba band into the superconductor. The main original result of this thesis is the derivation of an effective low-energy Kitaev-like Hamiltonian that describes the system as two 1D coupled channels.
Thanks to this model we achieved the main goal of this thesis: we are able to derive the phase diagram of the system by computing numerically the winding number w that shows that the system has different topological phases characterized by the presence (or absence) of multiple MFs. We discuss the role of disorder showing that the existence of multiple MF is related with the presence of the effective time-reversal symmetry. Finally, we study how the phase diagram changes in the small magnetization limit.
Our final statement is that the system can be topological and can host multiple MFs for certain conditions.
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